Question

Which is true for two vector A = A1i + A2j + A3k and B = B1i + B2j + B3k?

(a) A.B = A1B1 + A2B2 + A3B3

(b) AxB = A1B1 + A2B2 + A3B3

(c) A.B = A1B2 + A2B3 + A3B1

(d) AxB = A1B2 + A2B3 + A3B1

The question was posed to me in class test.

My query is from Dot Product and Cross Product topic in chapter Force Vectors of Engineering Mechanics

Answer 1

Correct option is (a) A.B = A1B1 + A2B2 + A3B3

For explanation I would say: The multiplication of x, y and z components with their respective same component give a scalar, equal to 1, i.e. i.i = 1 and j.j = 1, while jxj =0. This is the basic principle of the vector algebra which needs to apply wherever needed.